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Simplifying x2 + -20x + 86 = 0 Reorder the terms: 86 + -20x + x2 = 0 Solving 86 + -20x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-86' to each side of the equation. 86 + -20x + -86 + x2 = 0 + -86 Reorder the terms: 86 + -86 + -20x + x2 = 0 + -86 Combine like terms: 86 + -86 = 0 0 + -20x + x2 = 0 + -86 -20x + x2 = 0 + -86 Combine like terms: 0 + -86 = -86 -20x + x2 = -86 The x term is -20x. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20x + 100 + x2 = -86 + 100 Reorder the terms: 100 + -20x + x2 = -86 + 100 Combine like terms: -86 + 100 = 14 100 + -20x + x2 = 14 Factor a perfect square on the left side: (x + -10)(x + -10) = 14 Calculate the square root of the right side: 3.741657387 Break this problem into two subproblems by setting (x + -10) equal to 3.741657387 and -3.741657387.Subproblem 1
x + -10 = 3.741657387 Simplifying x + -10 = 3.741657387 Reorder the terms: -10 + x = 3.741657387 Solving -10 + x = 3.741657387 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = 3.741657387 + 10 Combine like terms: -10 + 10 = 0 0 + x = 3.741657387 + 10 x = 3.741657387 + 10 Combine like terms: 3.741657387 + 10 = 13.741657387 x = 13.741657387 Simplifying x = 13.741657387Subproblem 2
x + -10 = -3.741657387 Simplifying x + -10 = -3.741657387 Reorder the terms: -10 + x = -3.741657387 Solving -10 + x = -3.741657387 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = -3.741657387 + 10 Combine like terms: -10 + 10 = 0 0 + x = -3.741657387 + 10 x = -3.741657387 + 10 Combine like terms: -3.741657387 + 10 = 6.258342613 x = 6.258342613 Simplifying x = 6.258342613Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.741657387, 6.258342613}
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